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             α=3.0 —— Instance_25_1.0_3_1 —— 25 nodes       
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——————— Tue, 21 Mar 2023 17:03:46 ————————— 
ILP ——— 23 hubs —— 1—20—22—25—9—17—18—21—10—2—11—23—19—24—13—15—6—8—7—16—5—12—26
total time           17.68                gap                  0.0                  
LB <= UB             2146<=2146           subtour              0.0                  
connectivity cuts    73.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               2:25                 
2-opt strategy       0                                                              
nb. 2-opt            0.0                  n lazycuts edges     0.0                  
F                    100.0                post procedure       true                 
                                                                                                                                                                                                                                                            
Found solution
RING NODES
1—20—22—25—9—17—18—21—10—2—11—23—19—24—13—15—6—8—7—16—5—12—26

RING
1  --- 20 | cost [40.0]
1  --- 26 | cost [0.0]
2  --- 10 | cost [47.0]
2  --- 11 | cost [51.0]
5  --- 12 | cost [82.0]
5  --- 16 | cost [103.0]
6  ---  8 | cost [41.0]
6  --- 15 | cost [18.0]
7  ---  8 | cost [105.0]
7  --- 16 | cost [84.0]
9  --- 17 | cost [93.0]
9  --- 25 | cost [15.0]
10 --- 21 | cost [49.0]
11 --- 23 | cost [144.0]
12 --- 26 | cost [25.0]
13 --- 15 | cost [28.0]
13 --- 24 | cost [43.0]
17 --- 18 | cost [89.0]
18 --- 21 | cost [73.0]
19 --- 23 | cost [19.0]
19 --- 24 | cost [98.0]
20 --- 22 | cost [33.0]
22 --- 25 | cost [71.0]

STAR
3  -->  9 | cost [7.0]
4  --> 19 | cost [30.0]
14 --> 13 | cost [23.0]

BACKUP RING
1  --- 22 | cost [0.4]
2  --- 21 | cost [0.77]
2  --- 23 | cost [1.85]
5  ---  7 | cost [1.02]
5  --- 26 | cost [1.06]
6  ---  7 | cost [0.85]
6  --- 13 | cost [0.44]
8  --- 15 | cost [0.5700000000000001]
8  --- 16 | cost [1.6600000000000001]
9  --- 18 | cost [0.52]
9  --- 22 | cost [0.73]
10 --- 11 | cost [0.39]
10 --- 18 | cost [1.1300000000000001]
11 --- 19 | cost [1.44]
12 --- 16 | cost [1.37]
13 --- 19 | cost [1.21]
15 --- 24 | cost [0.43]
17 --- 21 | cost [1.57]
17 --- 25 | cost [1.08]
20 --- 25 | cost [0.8]
23 --- 24 | cost [1.09]

BACKUP STAR
3  --> 25 | cost [0.41000000000000003]
4  --> 23 | cost [0.73]
14 --> 15 | cost [0.84]

B = 1.85
i★ = 2
j★ = 11
k★ = 23

BD  —— 23 hubs —— 1-20-22-25-9-17-18-21-10-2-11-23-19-24-13-15-6-8-7-16-5-12-26-1
total time           9.21                 gap                  0.0                  
LB <= UB             2146<=2146           Master/SP costs      1961/185             
Master time          8.98                 SP time              0.24                 
subtour              0.0                  connectivity cuts    670.0                
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            284.0                SP method            poly                 
tildeV               2:25                 inst transformation  2                    
2-opt strategy       0                                                              
nb. 2-opt            0.0                  
F                    100.0                
                                                                                                                              
                                          
Found solution
RING NODES
1—20—22—25—9—17—18—21—10—2—11—23—19—24—13—15—6—8—7—16—5—12—26

RING
1  --- 20 | cost [40.0]
1  --- 26 | cost [0.0]
2  --- 10 | cost [47.0]
2  --- 11 | cost [51.0]
5  --- 12 | cost [82.0]
5  --- 16 | cost [103.0]
6  ---  8 | cost [41.0]
6  --- 15 | cost [18.0]
7  ---  8 | cost [105.0]
7  --- 16 | cost [84.0]
9  --- 17 | cost [93.0]
9  --- 25 | cost [15.0]
10 --- 21 | cost [49.0]
11 --- 23 | cost [144.0]
12 --- 26 | cost [25.0]
13 --- 15 | cost [28.0]
13 --- 24 | cost [43.0]
17 --- 18 | cost [89.0]
18 --- 21 | cost [73.0]
19 --- 23 | cost [19.0]
19 --- 24 | cost [98.0]
20 --- 22 | cost [33.0]
22 --- 25 | cost [71.0]

STAR
3  -->  9 | cost [7.0]
4  --> 19 | cost [30.0]
14 --> 13 | cost [23.0]

BACKUP RING
1  --- 22 | cost [0.4]
2  --- 21 | cost [0.77]
2  --- 23 | cost [1.85]
5  ---  7 | cost [1.02]
5  --- 26 | cost [1.06]
6  ---  7 | cost [0.85]
6  --- 13 | cost [0.44]
8  --- 15 | cost [0.5700000000000001]
8  --- 16 | cost [1.6600000000000001]
9  --- 18 | cost [0.52]
9  --- 22 | cost [0.73]
10 --- 11 | cost [0.39]
10 --- 18 | cost [1.1300000000000001]
11 --- 19 | cost [1.44]
12 --- 16 | cost [1.37]
13 --- 19 | cost [1.21]
15 --- 24 | cost [0.43]
17 --- 21 | cost [1.57]
17 --- 25 | cost [1.08]
20 --- 25 | cost [0.8]
23 --- 24 | cost [1.09]

BACKUP STAR
3  --> 25 | cost [0.41000000000000003]
4  --> 23 | cost [0.73]
14 --> 15 | cost [0.84]

B = 1.85
i★ = 2
j★ = 11
k★ = 23